
Re: Vindication of Goldbach's conjecture
Posted:
Jun 22, 2012 8:30 PM


On Jun 22, 11:14 am, mluttgens <lutt...@gmail.com> wrote: > On 22 juin, 13:05, Gus Gassmann <horand.gassm...@googlemail.com> > wrote: > > > > > > > > > > > On Jun 22, 7:40 am, mluttgens <lutt...@gmail.com> wrote: > > > > On 22 juin, 03:19, Gus Gassmann <horand.gassm...@googlemail.com> > > > wrote: > > > > > On Jun 21, 7:29 pm, mluttgens <lutt...@gmail.com> wrote: > > > > > > For N = 1000000, one gets 10804 Goldbach's pairs. > > > > > The relation between log N and log n is log n = 0.727*log N 0.436 > > > > > Note that this is not an equation, as it is not satisfied for N = 4. > > > > The linear relation has been calculated from N = 50 to N = 1000000. > > > Using it, one gets n = 8433 when N = 1000000, which is less than the > > > exact value 10804. > > > With the help of a graph, one could infer that another relationship, > > > probably exponential, would be more appropriate. This would of course > > > still clearer vindicate Goldbach's conjecture. > > > You chose not to respond to my main substantive point, which was that > > vindication =/= proof. Evidence in favor of the conjecture is hardly > > news. After all, the original conjecture was based on at least some > > evidence, so you are approximately 270 years too late. And since n(N), > > the number of ways one can partition N into primes, is not monotonic*, > > you cannot rule out a situation where N > 2 and n(N) = 0. > > > * n(8) = n(12) = 1, but n(10) = 2. > > And n(38) = 3, but you cannot find an even number N such as n(N) = 0! > > Why don't you react more positively instead of quibbling about the > meaning of proof. > > During those 270 years, nobody tried to correlate log N with log n.
Of course they have. Did you not even open up that wikipedia article I cited for you?
> If I had big computing power, I'd try numbers N = > 10^2, 10^3, etc... till for instance 10^15, and determine more > precisely the > curve linking the two logs. > If such curve confirms the positive correlation I found, it would not > only vindicate, > but also *prove* the validity of Goldbach's conjecture.
No, it would not. Unless you can show that the error in your formula is such that n is bounded away from zero, you have nothing. Vindication of the Goldbach conjecture is cheap, and it has been around for 270 years. A *proof* is elusive, and there one could make a definite name for oneself. First thing, of course, would be to acknowledge and understand the contributions of other, prior researchers.
YMMV.

